arXiv 1111.45202011-11math.ATmath-phmath.AGmath.DGmath.MP

The Cayley plane and String bordism

Carl McTague

备注：: 27 pages, significantly improved exposition following suggestions by Haynes Miller
发表信息：: Geom. Topol. 18 (2014) 2045-2078
DOI：: 10.2140/gt.2014.18.2045

英文摘要：

This paper shows that, away from 6, the kernel of the Witten genus is precisely the ideal consisting of (bordism classes of) Cayley plane bundles with connected structure group, but only after restricting the Witten genus to string bordism. It does so by showing that the divisibility properties of Cayley plane bundle characteristic numbers arising in Borel-Hirzebruch Lie-group-theoretic calculations correspond precisely to the divisibility properties arising in the Hovey-Ravenel-Wilson BP-Hopf-ring-theoretic calculation of string bordism at primes >3.

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